DC Circuit Equations

Ohm’s Law

V = IR
I = \frac{V}{R}
R = \frac{V}{I}

Joule’s Law

P = IV = \frac{V^2}{R} = I^2R

Resistors in Series and Parallel

Resistors in series increase the total equivalent resistance of the circuit:

R_{Tseries} = R_1+R_2+R_3+...+R_N

Resistors in parallel decrease the total equivalent resistance of the circuit:

R_{Tparallel} = \frac{1}{(\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}+...+\frac{1}{R_N})} = (\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}+...+\frac{1}{R_N})^{-1}

Capacitors in Series and Parallel

Capacitors in series decrease the total equivalent resistance of the circuit:

C_{Tseries} = \frac{1}{(\frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}+...+\frac{1}{C_N})} = (\frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}+...+\frac{1}{C_N})^{-1}

Capacitors in parallel increase the total equivalent resistance of the circuit:

C_{Tseries} = C_1+C_2+C_3+...+C_N